Einstein/Bohr Photon Box

[IM Egdall]

In 1930, Einstein made a famous argument against Heisenberg's Uncertainty Principle. Imagine a box with a photon inside and an opening covered by a shutter. When a timer attached to a clock activates the shutter, the photon escapes from the box. So we could in principle acurately time when the photon is emitted from the box.

 

Now this box is also suspended by a spring so that we can weigh the box before and after the photon is emitted. So, Einstein supposedly argued, we can determine the mass difference in the box. And by E=mc² the energy of the photon. So we now know both the time of photon emission and the photon's energy to arbitrary accuracy. But this is a violation of Heisenberg's Uncertainty Principle.

 

Bohr came up with a counter-argument. When the photon is emitted, the change in mass of the box causes it to rise on its springs. But due to gravitational time dilation, time runs a tiny bit faster at this higher altitude. Bohr calculated that this induces just the uncertainty in the clock's rate to satisfy the Uncertainty Principle. Borh and Quantum Mechanics wins!

 

A diagram of this is in: http://en.wikipedia....instein_debates (under Second Debate).

 

So here's my question. What if we conduct this thought experiment in outer space so far from any stellar objects that gravity is effectively zero? Here we use an Inertial Balance to measure the mass of the photon box before and after the photon is emitted. An Inertial Balance has the photon box suspended between two springs attached to fixed walls. You push the box to one side and let it go. It will then oscillate back and forth between the two springs. The frequency of oscillation of the box is a function of the spring constants and the mass of the box. See attachment: Inertial Balance Figure.ppt (The same concept is used to measure the mass of astronauts in space)

 

The difference in frequency of oscillation of the box before and after the photon is emitted gives us the change in mass of the box and hence the photon's energy. And since there is no gravity (spacetime curvature), there is no gravitational time dilation effect. Thus now the time of emission of the photon as recorded on the clock is known to arbitrary accuracy. So we now know both the photon's energy and time of emission to arbitrary accuracy; violating the Uncertainty Principle!

 

What is wrong with this argument? Perhaps there is no exactly zero gravity location at the Planck level. Or perhaps the Inertial Balance and its supports themselves provide a source of gravity? Do virtual particles have an effect? I'd like to hear any thoughts on this idea.

Edited October 22, 2010 by I ME

[swansont]

What about kinematic time dilation? The box is moving, owing to the oscillation, and must recoil when the photon is emitted.

[IM Egdall]

What about kinematic time dilation? The box is moving, owing to the oscillation, and must recoil when the photon is emitted.

 

 

Excellent point. So the change in motion of the box due to emission of the photon would affect the determination of time. I think that's it. Thanks.